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We study the collective modes of a confined gaseous cloud of bosons andfermions with mutual attractive interactions at zero temperature. The cloudconsists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside aspherical harmonic trap and the coupling between the two species is varied byincreasing either the magnitude of the interspecies s-wave scattering length orthe number of bosons. The mode frequencies are obtained in the collisionalregime by solving the equations of generalized hydrodynamics and are comparedwith the spectra calculated in the collisionless regime within a random-phaseapproximation. We find that, as the mixture is driven towards the collapseinstability, the frequencies of the modes of fermionic origin show a blue shiftwhich can become very significant for large numbers of bosons. Instead themodes of bosonic origin show a softening, which becomes most pronounced in thevery proximity of collapse. Explicit illustrations of these trends are givenfor the monopolar spectra, but similar trends are found for the dipolar andquadrupolar spectra except for the surface (n=0) modes which are essentiallyunaffected by the interactions.Comment: 9 pages, 5 figures, revtex

Collisional oscillations of trapped boson-fermion mixtures in the approach to the collapse instability